مرکز منطقه ای اطلاع رساني علوم و فناوري - Nonlinear feature extraction with a general criterion function

Abstract :

The optimal nonlinear features for a criterion function of the general form $f(D_{l},\\cdots ,D_{M},K_{1},\\cdots ,K_{M})$ are studied, where the $D_{j}$ and the are the conditional first- and second-order moments. The optimal solution is found to be a parametric function of the conditional densities. By imposing a further restriction on the functional dependence of $f$ on the $K_{j}$ , the optimal mapping becomes an intuitively pleasing function of the posterior probabilities. Given a finite number of features $\\psi_{1}(X),\\cdots ,\\psi_{L}(X)$ , the problem of finding the best linear mappings to $m$ features is next investigated. The resulting optimum mapping is a linear combination of the projections of the posterior probabilities onto the subspace spanned by the $\\psi_{j}(X)$ . The problem of finding the best single feature and seqnential feature selection is discussed in this framework. Finally, several examples are discussed.